Question

6. Let f(x) = x^2-1. Find (i) fof (ii) fofof​

Answer 1

Answer:

f(x) = x^2 - 1

(i) fof(x) = f[$x^{2}$ - 1]

            = ($x^{2}$ - 1)^2 - 1

            = $x^{4}$ - 2$x^{2}$ - 1 - 1

            = $x^{4}$ - 2$x^{2}$ - 2

(ii) fofof(x) = f{fof(x)}

                = f($x^{4}$ - 2$x^{2}$ - 2)

                = [$x^{4}$ - 2$x^{2}$ - 2]^2 - 1

                = $x^{8}$ + 8$x^{4}$ + 4 - 2$x^{6}$ + 4$x^{2}$ - 2$x^{4}$ - 1

By rearranging the terms:

               = $x^{8}$ - 2$x^{6}$ + $x^{4}$ - 2$x^{4}$ + 4$x^{2}$ + 4 - 1

               = $x^{8}$ - 2$x^{6}$ - $x^{4}$ + 4$x^{2}$ + 3